Isospin Multiplet Structure in Ultra--Heavy Fermion Bound States

Abstract

The coupled Bethe--Salpeter bound state equations for a $Q\bar Q$ system, where $Q=(U,D)$ is a degenerate, fourth generation, super--heavy quark doublet, are solved in several ladder approximation models. The exchanges of gluon, Higgs and Goldstone modes in the standard model are calculated in the ultra--heavy quark limit where weak $\gamma, W^\pm$ and $Z^0$ contributions are negligible. A natural $I=0$ and $I=1$ multiplet pattern is found, with large splittings occuring between the different weak iso--spin states when $M_Q$, the quark masses, are larger than values in the range $0.4 TeV<M_Q<0.8 TeV$, depending on which model is used. Consideration of ultra--heavy quark lifetime constraints and $U-D$ mass splitting constraints are reviewed to establish the plausibility of lifetime and mass degeneracy requirements assumed for this paper.